Question

The value of cos sec-1 5/3 is
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Answer 1

SOLUTION

TO DETERMINE

$\displaystyle \sf{ \cos { \sec}^{ - 1} \bigg( \frac{5}{3} \bigg)}$

EVALUATION

We have to determine

$\displaystyle \sf{ \cos { \sec}^{ - 1} \bigg( \frac{5}{3} \bigg)}$

Let

$\displaystyle \sf{ \theta = { \sec}^{ - 1} \bigg( \frac{5}{3} \bigg)}$

Then the given expression

$\displaystyle \sf{ \cos { \sec}^{ - 1} \bigg( \frac{5}{3} \bigg)}$

$= \displaystyle \sf{ \cos \theta }$

Now

$\displaystyle \sf{ \theta = { \sec}^{ - 1} \bigg( \frac{5}{3} \bigg)} \: \: gives$

$\implies \displaystyle \sf{ \sec \theta = \frac{5}{3} }$

$\implies \displaystyle \sf{ \cos \theta = \frac{3}{5} }$

Hence

$\displaystyle \sf{ \cos { \sec}^{ - 1} \bigg( \frac{5}{3} \bigg)} = \frac{3}{5}$

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